I will just say, that it depends on whom pick up the numbers.
It would differ if it's human or computers.
If it's computer the numbers will be totally random. If you have a large sample of computers involved, then the result will be around 50.
Now, when we are dealing with humans, the result will differ from 50 : it will show the interference of culture in the way we choose numbers.

I will just say, that it depends on whom pick up the numbers.
It would differ if it's human or computers.
If it's computer the numbers will be totally random. If you have a large sample of computers involved, then the result will be around 50.
Now, when we are dealing with humans, the result will differ from 50 : it will show the interference of culture in the way we choose numbers.

People.

Actually 100000 readers of a fairly liberal newspaper who can win $800 if they guess right

"I reject your reality and substitute it with my own" - President Bush

I've heard that "17" is the most commonly picked number, just straight-up. If that's so, then 12 would be a good choice. I'm not sure how the "2/3" would alter data. Presuming that everyone in the poll understands the question fully, the average will probably be lower than 50 itself, and the prize answer would be 2/3's of a number lower than fifty.

However, if everyone in the poll were like me, they'd all pick 0, and everyone would win.

Originally posted by SplinemodelI've heard that "17" is the most commonly picked number, just straight-up. If that's so, then 12 would be a good choice. I'm not sure how the "2/3" would alter data. Presuming that everyone in the poll understands the question fully, the average will probably be lower than 50 itself, and the prize answer would be 2/3's of a number lower than fifty.

However, if everyone in the poll were like me, they'd all pick 0, and everyone would win.

Splinemodel is correct.

The average of zero is zero and two thirds zero is zero.

"In a republic, voters may vote for the leaders they want, but they get the leaders they deserve."

It's not that difficult. The average (if everybody chose randomly) would be 50. But because people want to win they'll all choose 2/3 of 50. If everybody choses 2/3 of 50, the correct answer is no longer 2/3 of 50, it would be 2/3 of 2/3 of 50. And so on. So...
If you cannot pick decimals the answer is 1 (because 2/3 of 1 is closer to 1 than to 0)
If you can pick decimals the answer would be 0.
However, if you have to pick a number between 0 and 100 (and thus excluding 0 and 100) the most correct anser is something like 1 divided by infinity. Or actually the correct answer would be that there is no correct answer.
That. :-)

(and apparently Splinemodel agrees)

It's Better To Be Hated For What You Are Than To Be Loved For What You Are Not

And following that quasi recursive nature and applying the 80% rule for mass behaviors I estimated 30.47 as the magic number. I guess that could end up rounding/truncating to either side.

That assumes 80% will guess the average will be 50 and start with 2/3 of that, each remaining 20% recursively thinks they are smarter than the rest and guess based on the previous 80% rules types lower starting point. There is no mathematical rule that backs this up, but large samples unconsciously follow this sort of twisted logic all to readily.

why would anybody start with the idea the average is 50? That would imply some people would choose numbers in the 90s, and if I've understood the question properly that number cannot win. So no-one would choose it.

Same with 50 - for that number to win the average would be 75, correct? Which it wouldn't be.

A mathematician will instantly reply 0, but it won't be the right answer, of course.

I read about an economics teacher who presents the same problem for every new class. In his opinion, the problem parallels trading in the market. You always want to do your business ahead of the rest of the market. But you don't want to be ten years ahead, because you'll be bankrupt before a year is up. (These people were compared to ones who answer 0 in the game.)

No winning formula, but if I were you I'd google what kind of numbers have won previously with other groups of people. (If you do this, please share the numbers so we can use them later on!) Obviously the more mathematical the crowd and the more they expect others to recurse in their guess, the smaller the numbers. With the economics students the winning number was between 10 and 20 - so many of them had to assume their classmates only recurse one or two deep - but unfortunately I don't remember the exact number.

I would think it would depend on the sophistication of the game players.* The more sophisticated, the lower your guess, with a limit of the lowest possible number if you're playing against computers or game theoreticians (i.e., 1). The less sophisticated your opponents, the higher your guess, with a limit of 33 if you're playing against total dummies who generate random number guesses.

Playing against an average group of people, I'd assume the best guess would be in between those numbers somewhere, but I don't think there is any mathematical method of knowing where to guess in between 1 and 33. You'd need empirical data on what average people typically do in this situation.

Without any other data I'd just guess right in between 1 and 33 and say 17.

*[edit] It just occurred to me that it's not so much the sophistication of the players, but also their beliefs about the sophistication of their opponents. If you're playing with a large group of game theoreticians, and they all know they're playing with other game theoreticians, 1 is obviously the dominating response. But if you're playing with a group of game theoreticians who believe they're playing against a group of random-number generating chimpanzees, they'd all guess 33. Then you could come in and guess 33*.67=22, and take all the money.

Originally posted by BRussell
*[edit] It just occurred to me that it's not so much the sophistication of the players, but also their beliefs about the sophistication of their opponents. If you're playing with a large group of game theoreticians, and they all know they're playing with other game theoreticians, 1 is obviously the dominating response. But if you're playing with a group of game theoreticians who believe they're playing against a group of random-number generating chimpanzees, they'd all guess 33. Then you could come in and guess 33*.67=22, and take all the money.

That was actually pretty close. The right number was 21,6 (two thirds of the average 32,4), which actually chock me. Especially since 19.196 participated. Quite a lot of them must have chosen 33 as their answer (which could not ever have been the right answer) and almost for everyone betting lower than that there must have been someone betting higher (not adjusting for differences in the distance from the average on both sides).

"I reject your reality and substitute it with my own" - President Bush